text:
Silver Screen Beat
Phoenix readers: Win a pair of flex passes to the 2018 Phoenix Film Festival next month
'Parasite' becomes first foreign-language film to win best ensemble at the 2020 SAG Awards
Disney drops 'Fox' name from 20th Century Studios and Searchlight Pictures in rebranding effort
Quentin Tarantino says he has written and will direct five half-hour episodes of 'Bounty Law'
'The Lovebirds' trailer finds Kumail Nanjiani and Issa Rae trying to solve a bizarre murder case
Wes Anderson's new film 'The French Dispatch' is nowhere close to being four-hours-long
Season 2 of Jordan Peele's 'Twilight Zone' will star Billy Porter, Tony Hale, and Morena Baccarin
Bong Joon Ho and Adam McKay are bringing 'Parasite' to HBO in the form of a limited series
Netflix's 'Locke & Key' trailer reveals the long-awaited adaptation of the graphic novels
Jon Favreau confirms season two of 'The Mandalorian' will be coming to Disney Plus next fall
The film and television nominations for the 2020 Golden Globe Awards are officially in
'Midsommar' review: Ari Aster's disturbing cultish nightmare unfolds in broad, brilliant daylight
'Toy Story 4' review: Pixar's iconic franchise is back and it's warped, weird, and better for it
'Men in Black: International' review: You'll want to erase this movie from your mind after its over
'Rocketman' review: Elton John's biopic is so much better (and gayer) than 'Bohemian Rhapsody'
'Aladdin' review: Guy Ritchie's live-action remake of the Disney classic isn't exactly a whole new world
Margot Robbie returns as Harley Quinn in the excellent final trailer for Cathy Yan's 'Birds of Prey'
The lovely first trailer for Kelly Reichardt's 'Certain Women' follow-up 'First Cow' is finally here
The long-awaited first trailer for Christopher Nolan's new film 'Tenet' has finally arrived
Matt Casillas
GETTY IMAGES/FUSE
The 18th annual Phoenix Film Festival will return to Arizona on April 5-15 at Harkins Scottsdale 101 and we're giving one of our very lucky Phoenix-based readers the chance to win flex passes to the festival! With a flex pass, you and a guest will be able to choose four screenings to attend at the festival, except for the opening and closing night films.
Among the 150-plus movies screening at this year's Phoenix Film Festival are: Lean on Pete, Tully, Beirut, A Prayer Before Dawn, Hot Summer Nights, On Chesil Beach, Eighth Grade, A Kid Like Jake, The Last Movie Star, First Reformed, and Won't You Be My Neighbor. Click here to check out the complete lineup of films for this year's Phoenix Film Festival.
Enter here for your chance to win: http://bit.ly/2FkFcAU
Entries for this contest will close on March 30.
Related Topics:A Prayer Before DawnContestGiveawayHot Summer NightsLean on PetePhoenix Film FestivalTullyWon't You Be My Neighbor?
Ben Affleck and Oscar Isaac will lead the cast of Netflix's crime-thriller 'Triple Frontier'
'Avengers: Infinity War' broke Fandango's advance ticket sales record in just six hours
While nothing at last night's 2020 SAG Awards was particularly surprising — or exciting, for that matter — things did take a turn at the end of the show when it was announced that Parasite had won Outstanding Performance by a Cast in a Motion Picture.
Parasite stars Song Kang Ho, Lee Sun Kyun, Choi Woo Shik, Park So Dam, and Lee Jung Eun were on hand to accept the prize, which had never gone to a single foreign-language film in history until now.
"Although the title is Parasite, I think the story is about coexistence and how we can all live together," Song told the audience via a translator after receiving a standing ovation.
You can check out the complete list of 2020 SAG Awards winners below.
Outstanding Male Actor in a TV Movie or Limited Series
Mahershala Ali, True Detective
Russell Crowe, The Loudest Voice
Jharrel Jerome, When They See Us
Outstanding Female Actor in a TV Movie or Limited Series
Patricia Arquette, The Act
Michelle Williams, Fosse/Verdon
Outstanding Male Actor in a Comedy Series
Tony Shalhoub, The Marvelous Mrs. Maisel
Outstanding Female Actor in a Comedy Series
Alex Borstein, The Marvelous Mrs. Maisel
Catherine O'Hara, Schitt's Creek
Phoebe Waller-Bridge, Fleabag
Outstanding Comedy Ensemble
Outstanding Male Actor in a Drama Series
Steve Carell, The Morning Show
Billy Crudup, The Morning Show
Outstanding Female Actor in a Drama Series
Olivia Colman, The Crown
Elisabeth Moss, The Handmaid's Tale
Outstanding Drama Ensemble
Outstanding Performance by a Male Actor in a Supporting Role
Jamie Foxx, Just Mercy
Brad Pitt, Once Upon a Time in Hollywood
Outstanding Performance by a Female Actor in a Supporting Role
Laura Dern, Marriage Story
Scarlett Johansson, Jojo Rabbit
Nicole Kidman, Bombshell
Outstanding Performance by a Male Actor in a Leading Role
Taron Egerton, Rocketman
Joaquin Phoenix, Joker
Outstanding Performance by a Female Actor in a Leading Role
Lupita Nyong'o, Us
Renée Zellweger, Judy
Outstanding Performance by a Cast in a Motion Picture
Nearly a year after acquiring 21st Century Fox in a massive $71.3 billion dollar deal last March, the Walt Disney Company made the decision today to drop the "Fox" brand from two iconic Hollywood film studios: 20th Century Fox and Fox Searchlight Pictures.
As of today, 20th Century Fox will be known as 20th Century Studios, while Fox Searchlight Pictures has simply been rebranded Searchlight Pictures. The move isn't particularly surprising and was inevitable ever since last year's acquisition, but is still notable given 20th Century's 84-year history with the "Fox" brand attached to it.
While Disney wouldn't offer comment on its rebranding efforts, the change likely had to do with the fact that the company didn't want consumers to confuse its properties as being associated with Lachlan Murdoch's Fox Corporation, which operates the conservative media empire Fox News.
Despite the changes today, though, Disney will make minimal revisions to the iconic logos for the two studios. "The most notable change is that the word 'Fox' has been removed from the logo marks," reports Variety. "Otherwise, the signature elements — swirling klieg lights, monolith, triumphal fanfare — will remain the same."
Once Upon a Time in Hollywood director Quentin Tarantino has confirmed that he's bringing full five episodes of Bounty Law — the fictional Western series starring Leonardo DiCaprio's Rick Dalton — to the small screen.
During a recent interview with Deadline, the Oscar-winning filmmaker said that he will be directing five half-hour episodes of the show that have already been written, though it might be a while before we actually get to see them.
"It will take me a year and a half," Tarantino said. "[Bounty Law] got an introduction from Once Upon a Tim in Hollywood, but I don't really consider it part of that movie even though it is. This is not about Rick Dalton playing Jake Cahill. It's about Jake Cahill."
As for his inspiration for Bounty Law, Tarantino added: "Where all this came from was, I ended up watching a bunch of Wanted, Dead or Alive, and The Rifleman, and Tales of Wells Fargo, these half-hour shows to get in the mindset of Bounty Law, the kind of show Rick was on. I'd liked them before, but I got really into them."
Whether or not DiCaprio will reprise his role as Rick Dalton for Bounty Law remains to be seen, but I can't imagine why he wouldn't. After all, Dalton is the star of the show and it really wouldn't be the same without his involvement.
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text:
P4 Radio Hele Norge (kurz P4) ist Norwegens größter kommerzieller Radiosender mit 24 % Marktanteil, etwa einer Million täglicher Zuhörer und zwei Millionen pro Woche, weit mehr, als der zweitgrößte Privatsender Radio Norge erreicht. Das Unternehmen mit Sitz in Lillehammer gehört zur Nordic Entertainment Group, einer Ausgründung der Modern Times Group. Weitere Studios befinden sich in Oslo, Bergen, Tromsø und Kristiansand.

Gegründet wurde der Sender im Jahr 1993. Er sendet via FM, DAB und über das Internet.

Radiokanäle und Programme

P4 sendet neben P4 Norge (via FM, DAB und Internet) noch folgende Internetkanäle:

 P4 Jukebox
 P4 Radio Retro
 P4 Hits
 P4 Ballade
 P4 Bandit
 P4 Julekanalen (Weihnachtskanal – 1. bis 31. Dezember)

Folgende Radioprogramme von P4 erreichten laut Gallup Umfrage 2009 folgende Reichweiten:

 P4s radiofrokost, 658.000 Zuhörer, 19,5 % Marktanteil
 Midt i trafikken, 581.000 Zuhörer, 23,7 % Marktanteil
 Ett-to-tre, 490.000 Zuhörer, 24,9 % Marktanteil
 Michael direkte, 389.000 Zuhörer, 22,7 % Marktanteil
 Taxi, 281.000 Zuhörer, 25,0 % Marktanteil
 Sytten tretti, 157.000 Zuhörer, 22,5 % Marktanteil
 Kveldsshowet, 137.000 Zuhörer, 19,4 % Marktanteil
 Barnas Beste, 119.000 Zuhörer, 29,7 % Marktanteil

Weblinks

 P4.no
 Bandit

Hörfunksender (Norwegen)
Lillehammer
Privater Hörfunksender
Gegründet 1993

redpajama_set_name: RedPajamaWikipedia


Check out our Director, Linda Kuo in the Mark Morris Dance Center blog!
DUNYC The Company invites professional and aspiring dancers to our open rehearsals. The goal of our open rehearsals is to share our vision and training with our community, and providing a network for dancers to connect.
Dancers from open rehearsals have been invited to perform with our company in the past. Some of our current company dancers were also scouted from our open rehearsals.
All open rehearsals are pay-as-you-can donations classes. ALL proceeds go to the teaching faculty. Space is limited; RSVP strongly recommended.
Don't forget to purchase tickets for our upcoming studio showcase on April 16, 2016!
TWCP connects artists and humanitarian projects to empower communities and individuals. Check out what we have been up to and join our upcoming tour to Hawaii, Cambodia, Thailand and Nepal!
We are back in Shanghai for Battle In Shanghai!
Hawaii's own Bboy Joshskittle, winner of our Hawaii qualifier, will be entering the World Finals in Shanghai for the 2nd time!
This year, DU teams up with The World Collaboration Project and Altruglobal in Shanghai to empower communities using the values of HIP HOP: "Peace, Love, Unity, and Having Fun." Stay tuned for our outreach and battle videos!


text:
Фу () — громада  в Швейцарії в кантоні Во, округ Бруа-Вюлі.

Географія
Громада розташована на відстані близько 29 км на захід від Берна, 55 км на північний схід від Лозанни.
Фу має площу 3,5 км², з яких на 19,2% дозволяється будівництво (житлове та будівництво доріг), 54,7% використовуються в сільськогосподарських цілях, 24,9% зайнято лісами, 1,1% не є продуктивними (річки, льодовики або гори).

Демографія

2019 року в громаді мешкало 881 особа (+19,1% порівняно з 2010 роком), іноземців було 17,8%. Густота населення становила 253 осіб/км².
За віковим діапазоном населення розподілялося таким чином: 21,2% — особи молодші 20 років, 64,1% — особи у віці 20—64 років, 14,6% — особи у віці 65 років та старші. Було 403 помешкань (у середньому 2,2 особи в помешканні).
Із загальної кількості 174 працюючих 27 було зайнятих в первинному секторі, 35 — в обробній промисловості, 112 — в галузі послуг.

Примітки

Громади Во


text:
Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000
The instance Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000 represents a material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
The Resource Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000
agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000
Context of Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000

 Data from Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000 - University of Missouri-St. Louis Libraries

Data Citation of the Instance Defense, North American Aerospace Defense Command (NORAD) : agreement between the United States of America and Canada, effected by exchange of notes, signed at Washington March 28, 1996 and extending agreement, effected by exchange of notes, signed at Washington June 16, 2000

redpajama_set_name: RedPajamaCommonCrawl


text:
Marcel Mauri de los Rios (Badalona, 1977) és un historiador i periodista català que actualment exerceix de vicepresident primer i portaveu d'Òmnium Cultural.

Biografia
Va néixer a Badalona el 1977, sent el petit de tres fills d'una família treballadora. Mauri va estudiar a l'Escola Jungfrau i a l'institut La Llauna de Badalona i des de ben jove va entrar en contacte amb el món associatiu: primer, en l'àmbit de l'esplai; més endavant, ja a la universitat, amb el Bloc d'Estudiants Independentistes (BEI) i la Coordinadora d'Estudiants dels Països Catalans (CEPC).

Trajectòria acadèmica i professional
És doctor en periodisme per la Universitat Pompeu Fabra i llicenciat en història per la Universitat Autònoma de Barcelona. Des de l'any 2002 és professor d'Història del periodisme i l'ètica periodística en el Departament de Comunicació de la Universitat Pompeu Fabra. També és consultor de l'ètica i el dret de comunicació a la Universitat Oberta de Catalunya. El 2007 va dur a terme la recerca predoctoral a la Universitat de la Sorbona de París, el 2010 va realitzar una investigació postdoctoral a la Universitat de Colúmbia de Nova York. Ha publicat articles i llibres sobre ètica dels mitjans i història del periodisme.

El 8 de gener de 2016 fou escollit cap de gabinet d'Alcaldia i Comunicació de l'Ajuntament de Badalona. El setembre del 2017 fou nomenat assessor del vicepresident i conseller d'Economia i Hisenda del Govern de Catalunya, Oriol Junqueras. Arran de la detenció de Jordi Cuixart, Mauri va adquirir més protagonisme com a portaveu d'Òmnium.

Activisme
Des de la infància ha estat vinculat al moviment associatiu de la ciutat de Badalona, iniciant-se primer com a monitor i director de l'esplai Cra-Crac, i més endavant, sent un dels impulsors de la plataforma "Badalona Som Totes i Tots" creada per fomentar la cohesió social i la integració de les persones nouvingudes a la ciutat. L'any 2000 va fer una estada com a cooperant a la universitat d'El Salvador en projectes de ràdios i mitjans comunitaris. Va ser membre de la Coordinadora d'Associacions per la Llengua Catalana (CAL) a Badalona i va treballar a l'àrea de comunicació de la Fundació Pere Tarrés.

Òmnium Cultural
Des de l'any 2007 va formar part de la junta territorial d'Òmnium Badalona - Barcelonès Nord, sent-ne el president durant gairebé 4 anys (2010-2014). L'any 2014 va dimitir per formar part de la candidatura de Muriel Casals a la Junta directiva nacional d'Òmnium Cultural, càrrec voluntari i no remunerat. Va ser vocal de la Junta directiva fins que el 16 d'octubre de 2017 van empresonar Jordi Cuixart a Soto del Real, quan va passar a ser vicepresident i portaveu de l'entitat, càrrecs també, no remunerats.

Premis i reconeixements
L'any 2012 va ser guardonat amb el Premi de Comunicació Social Joan Givanel i Mas de l'Institut d'Estudis Catalans.

Referències

Periodistes catalans
Independentistes catalans
Socis d'Òmnium Cultural
Periodistes badalonins
Historiadors badalonins
Alumnes de la Universitat Pompeu Fabra
Alumnes de la Universitat Autònoma de Barcelona
Activistes badalonins
Historiadors del Barcelonès contemporanis
Activistes catalans del sud contemporanis


Nikhil Advani ropes in Kangana Ranaut to play cop in his next! Nikhil Advani ropes in Kangana Ranaut to play cop in his next!
Home > upcoming movies > Nikhil Advani ropes in Kangana Ranaut to play cop in his next!
Nikhil Advani ropes in Kangana Ranaut to play cop in his next!
Queen's latest movie Katti Batti (Nikhil Advani's directorial) is all set to release, and now we hear that Queen will be again working in Nikhil's film! The director have roped in Kangana to play a cop in his upcoming film which is supposedly a thriller film.
The film is based on a Hollywood thriller The Girl with the Dragon Tattoo. When Nikhil narrated the script to Kangana, she immediately said yes to it!
Commenting on the same Nikhil says, "Yes Kangna will be featuring in my next, but it is still too early to talk about it. As of now, I can say that Kangna will be undergoing workshops on mannerisms and her body language for the film."
Kangana is very excited to work with Nikhil once again! The film is supposed to go on floors by next year. She has also been signed up for Ketan Mehta's "Rani Laxmibai" and Hansal Mehta's "Simran".


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The knife rack safely and easily holds knives of any material (ceramic, steel, etc.).
Rods allow holding the knife at any angle.
The knife holder can accommodate up to 10 knives (depends on the size of the knife) and is suitable for blades of up to 20cm from a small paring knife to a chef knife.


text:
\section{#1}%
     \renewcommand{\thesection}{\Alph{section}} }

\begin{document}

\title{HQET renormalization group improved Lagrangian at $\mathcal{O}(1/m^3)$ with leading logarithmic accuracy: Spin-dependent case}
\author{Xabier Lobregat}
\email{lobregat@ifae.es }
\author{Daniel Moreno}
\email{dmoreno@ifae.es}
\address{Grup de F\'\i sica Te\`orica, Dept. F\'\i sica and IFAE-BIST, Universitat Aut\`onoma de Barcelona,\\
E-08193 Bellaterra (Barcelona), Spain}
\author{Rudin Petrossian-Byrne}
\email{rudin.petrossian-byrne@physics.ox.ac.uk}
\address{Rudolf Peierls Centre for Theoretical Physics, University of Oxford,
1 Keble Road, Oxford OX1 3NP, United Kingdom}
\date{\today}

\begin{abstract}
We obtain the renormalization group improved expressions of the Wilson coefficients associated to the  ${\cal O}(1/m^3)$ spin-dependent heavy quark
effective theory Lagrangian operators, with leading logarithmic approximation, in the case of zero light quarks. We have employed the Coulomb gauge.
\end{abstract}
\maketitle

\section{Introduction}

The expansion in inverse powers of the heavy quark mass is a useful tool for the study of hadrons containing heavy quarks. This expansion can be formulated more systematically in terms of an effective theory
described by an effective Lagrangian. For the one-heavy quark sector this
theory is heavy quark effective theory (HQET) \cite{HQET}. The HQET Lagrangian is also a key object in the description of systems with more than one heavy quark, in particular
in the description of the heavy quark-antiquark sector (i.e. heavy quarkonium), since the HQET Lagrangian corresponds to one of the building blocks of the
nonrelativistic QCD (NRQCD) Lagrangian~\cite{NRQCD,Bodwin:1994jh}. The Wilson coefficients of the HQET Lagrangian also enter into
the Wilson coefficients of the operators (i.e. the potentials) of the pNRQCD Lagrangian \cite{Pineda:1997bj,Brambilla:1999xf},
an effective field theory optimised for the description of heavy quarkonium systems near threshold (for reviews
see Refs. \cite{Brambilla:2004jw,Pineda:2011dg}). The Wilson coefficients we compute in this paper
are necessary ingredients to obtain the pNRQCD Lagrangian with next-to-next-to-next-to-leading logarithmic (NNNLL) accuracy. It should be noted that the Wilson coefficients computed in this paper are not necessary to obtain the
complete heavy quarkonium spectrum with NNNLL accuracy, nor the production and annihilation of heavy quarkonium with NNLL
precision, unlike their spin-independent counterparts (see Ref. \cite{rgsddelta,inpreparation}), but they may become important at the next order. At least,
they must be studied. These results are also instrumental in the determination of higher order
logarithms for NRQED bound states, such as hydrogen and muonic hydrogen-like atoms.

At present, the operator structure of the HQET Lagrangian, and the tree-level values of their Wilson coefficients, is known to ${\cal O}(1/m^3)$ in
the case without massless  quarks \cite{Manohar:1997qy}. The inclusion of massless quarks has been considered in Ref. \cite{Balzereit:1998am}.
The Wilson coefficients with leading logarithmic (LL) accuracy were computed in Refs. \cite{Finkemeier:1996uu,Blok:1996iz,Bauer:1997gs}
to ${\cal O}(1/m^2)$ and at next-to-leading order (NLO) in Ref. \cite{Manohar:1997qy} to ${\cal O}(1/m^2)$ (without dimension 6 heavy-light operators). The LL
running to ${\cal O}(1/m^3)$ without the inclusion of spectator quarks was considered in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}, which turned out
to have internal discrepancies between their explicit single log results and their own anomalous dimension matrix. The computation was reconsidered in
Ref. \cite{chromopolarizabilities}, where the spin-independent results were corrected. This work is a follow-up to
Ref. \cite{chromopolarizabilities} and, for this reason, is structured very similarly. Here we focus on spin-dependent operators and obtain the renormalization group improved Wilson coefficients of the HQET Lagrangian with LL
accuracy to $\mathcal{O}(1/m^3)$. We do not include light quarks in our analysis.

The paper is divided as follows. In Sec. \ref{Sec:Lag} we introduce the HQET Lagrangian. Sec. \ref{Sec:Compton} is dedicated to the study of
the spin-dependent part of Compton scattering, performed in order to find physical combinations of Wilson coefficients. In Sec. \ref{Sec:RGE} we find the
renormalization group equations (RGE) for these Wilson coefficients. The QCD case is considered in Sec. \ref{sec:RGeq}, and the QED case
in Sec. \ref{sec:RGeqqed}. The solution of these equations is studied in Sec. \ref{Sec:numerics}. In Sec \ref{Sec:Comparison} we perform a detailed
comparison between our results and the ones found in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}. Our conclusions are summarized in Sec. \ref{sec:conclusions}. Finally, in
App. \ref{sec:fr} we present some new Feynman rules needed for the computation.

\section{HQET Lagrangian without light fermions}
\label{Sec:Lag}

The HQET Lagrangian is defined uniquely up to field redefinitions.
In this paper we use the HQET Lagrangian density for a quark of mass $ m \gg \Lambda_{\rm QCD}$, in the special frame $v=(1,0,0,0)$ given in
Ref. \cite{Manohar:1997qy}:
\begin{eqnarray}
&&
{\cal L}_{\rm HQET}={\cal L}_g+{\cal L}_{Q}
\,,
\label{LagHQET}
\\
\nonumber
\\
&&
{\cal L}_g=-\frac{1}{4}G^{\mu\nu \, a}G_{\mu \nu}^a +
c_1^{g}\frac{g}{4m^2}
 f^{abc} G_{\mu\nu}^a G^{\mu \, b}{}_\alpha G^{\nu\alpha\, c}+
{\cal O}\left(\frac{1}{m^4}\right),
\label{Lg}
\\
\nonumber
\\
&&
\nonumber
{\cal L}_{Q}=
Q^{\dagger} \Biggl\{ i D_0 + \frac{c_k}{ 2 m} {\bf D}^2
+ \frac{c_F }{ 2 m} {\mbox{\boldmath $\sigma$} \cdot g{\bf B}}
\\
&& \nonumber
+\frac { c_D}{ 8 m^2} \left({\bf D} \cdot g{\bf E} - g{\bf E} \cdot {\bf D} \right) + i \, \frac{ c_S}{ 8 m^2}
{\mbox{\boldmath $\sigma$} \cdot \left({\bf D} \times g{\bf E} -g{\bf E} \times {\bf D}\right) }
\\
&& \nonumber
+\frac {c_4 }{ 8 m^3} {\bf D}^4 + i c_M\, g { {\bf D\cdot \left[D \times B
\right] + \left[D \times B \right]\cdot D} \over 8 m^3}
+ c_{A_1}\, {g^2}\, {{\bf B}^2-{\bf E}^2 \over 8 m^3}-
c_{A_2} { {g^2}{\bf E}^2 \over 16 m^3}
\\
&& + c_{W_1}\, g { \left\{ {\bf D^2,\mbox{\boldmath $\sigma$}
\cdot B }\right\}\over 8 m^3} - c_{W_2}\, g { {\bf D}^i\, {\bf \mbox{\boldmath $\sigma$}
\cdot B} \, {\bf D}^i  \over 4 m^3}+ c_{p'p}\, g { {\bf \mbox{\boldmath $\sigma$} \cdot D\, B \cdot D + D
\cdot B\, \mbox{\boldmath $\sigma$} \cdot D}\over 8 m^3}
\nonumber
\\
&&
+ c_{A_3}\, {g^2}\, \frac{1}{N_c}{\rm Tr}\left({{\bf B}^2-{\bf E}^2 \over 8 m^3}\right)-
c_{A_4}\, {g^2}\, \frac{1}{N_c}{\rm Tr}\left({{\bf E}^2 \over 16 m^3}\right)
\nonumber
\\
&&
+ i c_{B_1}\, g^2\, { {\bf \mbox{\boldmath $\sigma$} \cdot \left(B
\times B - E \times E \right)} \over 8 m^3}
- i c_{B_2}\, g^2\, { {\bf \mbox{\boldmath $\sigma$} \cdot \left( E \times E \right)} \over 8 m^3}
\Biggr\} Q+
{\cal O}\left(\frac{1}{m^4}\right)

\,.
\label{Lhh}
\end{eqnarray}
Where $Q$ is the NR fermion field represented by a Pauli spinor. The components of the vector $\mbox{\boldmath $\sigma$}$ are the Pauli matrices. We define
$i D^0=i\partial^0 -gA^0$, $i{\bf D}=i\mbox{\boldmath $\nabla$}+g{\bf A}$,
${\bf E}^i = G^{i0}$ and ${\bf B}^i = -\epsilon^{ijk}G^{jk}/2$, where $\epsilon^{ijk}$ is
the three-dimensional totally antisymmetric tensor\footnote{
In dimensional regularization several prescriptions are possible for the $\epsilon^{ijk}$ tensors and $\mbox{\boldmath $\sigma$}$, and the same prescription
as for the calculation of the Wilson coefficients must be used.}
with $\epsilon^{123}=1$ and $({\bf a} \times {\bf b})^i \equiv \epsilon^{ijk} {\bf a}^j {\bf b}^k$. Note also that we have rescaled by a factor $1/N_c$ the
coefficients $c_{A_{3,4}}$ following Ref. \cite{chromopolarizabilities}, as compared to the definitions given in Ref. \cite{Manohar:1997qy}.

\section{Compton scattering}
\label{Sec:Compton}

Ref. \cite{chromopolarizabilities} showed that it is possible for the Wilson coefficients
associated to $1/m^3$ operators to be gauge dependent. For example, this is the case for $c_{A_2}$, which always appears in physical observables along
with $c_M$ (well-known to be gauge dependent because it is related with $c_D$ through reparametrization invariance, Ref. \cite{Manohar:1997qy}) in such a way
that the combination
is gauge independent/physical. In order to explore the existence of other physical combinations involving the Wilson coefficients that we aim to
calculate , i.e. $c_{W_1}$, $c_{W_2}$, $c_{p'p}$, $c_{B_1}$ and $c_{B_2}$, we compute the amplitude for Compton scattering of a heavy quark with a gluon $Qg\rightarrow Qg$.
In this section, we restrict to the the spin-dependent part of this process in HQET. We compute it at tree level up to $\mathcal{O}(1/m^3)$ in the mass expansion and in the Coulomb gauge
(though obviously the amplitude for Compton scattering is a gauge independent quantity).
We take incoming and
outgoing quarks to have four-momentum $p=(E_1,\bf p)$ and $p'=(E_1',\bf p\,')$. We take gluon four-momenta as outgoing and label them
by $k_1$, $i$, $a$ and $k_2$, $j$, $b$ with respect to color and vector indices. This also implies the on-shell condition
$k_1^0= -|\bf k_1|$ and $k_2^0= |\bf k_2|$. We work in the incoming quark rest frame, i.e $E_1=0$ and $\bf p=0$, so $\bf p\,'=-(\bf k_1 + \bf k_2)$
and $E_1'=-(k_1^0 + k_2^0)$. In addition, we define the unit vectors $\bf n_1=\bf k_1/|\bf k_1|$ and
$\bf n_2=\bf k_2/|\bf k_2|$. The relation
\begin{equation}
 |{\bf k}_2|=\frac{|{\bf k}_1|}{1+\frac{|{\bf k}_1|}{m}(1 + {\bf n}_1\cdot{\bf n}_2)}
\end{equation}
holds from four-momenta conservation.

\begin{figure}[!htb]

	\includegraphics[width=0.80\textwidth]{Compton.png}

	%
	%

	%
\caption{Topologies contributing to Compton scattering at tree level up to ${\cal O}(1/m^3)$. Diagrams are generated from these topologies
by considering all possible vertices contributing up to ${\cal O}(1/m^3)$.
\label{PlotsCompton}}
\end{figure}

By inserting the appropiate Wilson coefficients up to ${\cal O}(1/m^3)$, the topologies of the diagrams we have to consider for this computation are listed in Fig.~\ref{PlotsCompton}. The amplitude reads:

$$\mathcal{A}^{ij\,ab} = (c_{B_1}-2c_{W_1}- c_F^2 c_k  -c_S c_k)\frac{g^2}{16m^3}|{\bf k}_1|^2
( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1){\bf n}_2^k \epsilon^{ijk}
 + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_1^k \epsilon^{ijk} $$
$$+ \mbox{\boldmath $\sigma$}^i ({\bf n}_1\times{\bf n}_2)^j
+ \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i] [T^a,T^b]_{\alpha\beta}$$
$$-  (2c_{W_1} - 2c_{W_2}  +2c_F c_k^2 + c_S c_k + c_S c_F)\frac{g^2}{16m^3}|{\bf k}_1|^2
( (\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j - (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i )[T^a,T^b]_{\alpha\beta} $$
$$-  (2c_{W_1} - 2c_{W_2} - c_S c_F + c_S c_k - 2c_F c_k^2)
\frac{g^2}{16m^3}|{\bf k}_1|^2 ( (\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j + (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)\{T^a,T^b\}_{\alpha\beta}$$
$$+  ( c_{B_2} + c_{B_1} -2c_{W_1} - c_S c_F -c_S c_k)\frac{g^2}{8m^3}|{\bf k}_1|^2 \mbox{\boldmath $\sigma$}^k \epsilon^{ijk} [T^a,T^b]_{\alpha\beta}$$
$$ - c_{p'p}\frac{g^2}{16m^3}|{\bf k}_1|^2
[(  ({\bf n}_1\times{\bf n}_2)^j \mbox{\boldmath $\sigma$}^i - ({\bf n}_1\times{\bf n}_2)^i \mbox{\boldmath $\sigma$}^j
+ \epsilon^{ijk}({\bf n}_1-{\bf n}_2)^k(\mbox{\boldmath $\sigma$}\cdot({\bf n}_1+{\bf n}_2)))\{T^a,T^b\}_{\alpha\beta} $$
$$ - (  ({\bf n}_1\times{\bf n}_2)^j \mbox{\boldmath $\sigma$}^i + ({\bf n}_1\times{\bf n}_2)^i\mbox{\boldmath $\sigma$}^j
 - \epsilon^{ijk}({\bf n}_1 + {\bf n}_2)^k(\mbox{\boldmath $\sigma$}\cdot({\bf n}_1 + {\bf n}_2)))[T^a,T^b]_{\alpha\beta}]$$
$$ + c_S c_k\frac{g^2}{8m^3}|{\bf k}_1|^2(1+ {\bf n}_1\cdot{\bf n}_2)\mbox{\boldmath $\sigma$}^k \epsilon^{ijk} [T^a,T^b]_{\alpha\beta}$$
$$ +  c_F^2\frac{g^2}{8m^3} |{\bf k}_1|^2(1 + {\bf n}_1\cdot{\bf n}_2)
 ( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}  + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i )[T^a,T^b]_{\alpha\beta}$$
$$- c_F c_k \frac{g^2}{4m^3}|{\bf k}_1|^2 (1 + {\bf n}_1\cdot{\bf n}_2) (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i  [T^a,T^b]_{\alpha\beta}$$
$$ - \frac{g^2}{8m^3} |{\bf k}_1|^2(1 + {\bf n}_1\cdot{\bf n}_2)
[c_S((\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk})
+ c_F^2( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}  + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i )$$
$$- 2c_F c_k(\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i] \{T^a,T^b\}_{\alpha\beta}$$
$$+ \frac{g^2}{8m^2}|{\bf k}_1|[(2c_F c_k - c_S c_k)((\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j - (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)
+ c_S c_k( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1){\bf n}_1^k \epsilon^{ijk} +(\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk})$$
$$+ c_F^2( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1) {\bf n}_2^k \epsilon^{ijk}  + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}
+ \mbox{\boldmath $\sigma$}^i ({\bf n}_1\times{\bf n}_2)^j + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i)] \{T^a, T^b\}_{\alpha\beta}$$
$$+  c_F c_k \frac{g^2}{4m^2} |{\bf k}_1|((\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j + (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)[T^a,T^b]_{\alpha\beta}$$
$$+ c_F\frac{g^2}{2m}\mbox{\boldmath $\sigma$}^k \epsilon^{ijk}[T^a,T^b]_{\alpha\beta}$$
$$+ c_F \frac{g^2}{4m} \frac{1}{1+{\bf n}_1\cdot{\bf n}_2}
(( \mbox{\boldmath $\sigma$}\times{\bf n}_2)^i {\bf n}_1^j
 - (\mbox{\boldmath $\sigma$}\times{\bf n}_1)^j {\bf n}_2^i
 + \mbox{\boldmath $\sigma$}^i ({\bf n}_1\times{\bf n}_2)^j
 + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i$$
\begin{equation}
 + 2(\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j
 - 2(\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)[T^a,T^b]_{\alpha\beta}\,.
\end{equation}
Note that $c_D$ does not appear explicitely. One can also observe that two combinations always appear in the observable:
$\bar c_W \equiv c_{W_1}-c_{W_2}$ and $\bar c_{B_1}\equiv c_{B_1}-2c_{W_1}$. These, together with $c_{B_2}$ and $c_{p'p}$, are physical combinations,
i.e. they are gauge independent. This implies that the renormalization group equations (RGE) of these physical combinations can only depend
on physical combinations of Wilson coefficients. Later on we will see that this is indeed the case. We suspect that individually
$c_{W_1}$, $c_{W_2}$ and $c_{B_1}$ are gauge dependent quantities, since we are in agreement with Ref. \cite{Balzereit:1998jb}, where the calculation was done
in Feynman gauge, at the level of single logs for physical combinations but we disagree for each of these three individually.

For QED we obtain

$$\mathcal{A}^{ij} = \frac{g^2}{4m^2}|{\bf k}_1|[(2c_F c_k - c_S)((\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j - (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)
+ c_S( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1){\bf n}_1^k \epsilon^{ijk} +(\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk})$$
$$+ c_F^2( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1) {\bf n}_2^k \epsilon^{ijk}  + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}
+ \mbox{\boldmath $\sigma$}^i ({\bf n}_1\times{\bf n}_2)^j + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i)]$$
$$-  (2c_{W_1} - 2c_{W_2} - c_S c_F + c_S c_k - 2c_F c_k^2)
\frac{g^2}{8m^3}|{\bf k}_1|^2 ( (\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j + (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i)$$
$$ -c_{p'p}\frac{g^2}{8m^3}|{\bf k}_1|^2
(({\bf n}_1\times{\bf n}_2)^j \mbox{\boldmath $\sigma$}^i - ({\bf n}_1\times{\bf n}_2)^i \mbox{\boldmath $\sigma$}^j
+ \epsilon^{ijk}({\bf n}_1-{\bf n}_2)^k(\mbox{\boldmath $\sigma$}\cdot({\bf n}_1+{\bf n}_2)))$$
$$ - \frac{g^2}{4m^3} |{\bf k}_1|^2(1 + {\bf n}_1\cdot{\bf n}_2)
[c_S(( \mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk})
+ c_F^2( (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}  + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i )$$
\begin{equation}
 - 2c_F c_k(\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i]\,.
\end{equation}
Note that there is no ${\cal O}(1/m^0,1/m)$ contribution. Setting the Wilson coefficients to their tree level values we obtain

$$\mathcal{A}^{ij} = \frac{g^2}{4m^2}|{\bf k}_1|[ (\mbox{\boldmath $\sigma$}\times{\bf n}_1)^i {\bf n}_1^j - (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i
+  (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1){\bf n}_1^k \epsilon^{ijk} + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk}$$
$$+  (\mbox{\boldmath $\sigma$}\cdot{\bf n}_1) {\bf n}_2^k \epsilon^{ijk}  + (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}
+ \mbox{\boldmath $\sigma$}^i ({\bf n}_1\times{\bf n}_2)^j + \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i]$$
\begin{equation}
 + \frac{g^2}{4m^3} |{\bf k}_1|^2(1 + {\bf n}_1\cdot{\bf n}_2)
( - \mbox{\boldmath $\sigma$}^j ({\bf n}_1\times{\bf n}_2)^i -  (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2) {\bf n}_1^k \epsilon^{ijk}
+ (\mbox{\boldmath $\sigma$}\times{\bf n}_2)^j {\bf n}_2^i - (\mbox{\boldmath $\sigma$}\cdot{\bf n}_2){\bf n}_2^k \epsilon^{ijk})\,.
\end{equation}
This expression agrees with Eq. (19) in Ref. \cite{Balk:1993ev}.

The above analysis gives us the set of Wilson coefficients and their combinations that appear in physical observables: $\{\bar c_{W},\bar c_{B_1},c_{B_2},c_{p'p}\}$.
We compute the anomalous dimensions for these, but also for the unphysical set: $\{c_{W_1}, c_{W_2},c_{B_1},c_{B_2},c_{p'p}\}$, in
Coulomb gauge, as it can be important for future research investigating the possible gauge dependence of these Wilson coefficients.

\section{Anomalous dimensions for $1/m^3$ spin-dependent operators}
\label{Sec:RGE}

In this section we determine the anomalous dimensions of the Wilson coefficients associated to $1/m^3$ spin-dependent operators with ${\cal O}(\alpha)$
accuracy. In principle, one would like to only compute irreducible diagrams. However, as indicated in Ref. \cite{chromopolarizabilities}, this would involve
considering a more extensive basis of operators, including those that vanish on shell. Instead, since we want to work in a minimal
basis of operators, we will also need to consider reducible diagrams in a computation that resembles that of an S-matrix element. In particular, we will compute the divergent part of the amplitude for elastic scattering of the heavy quark with a
tranverse gluon at one-loop. These divergences cancel with the divergences of the Wilson coefficients determining the anomalous dimension. The computation
is organized in powers of $1/m$, up to ${\cal O}(1/m^3)$, by considering all possible insertions of the HQET Lagrangian operators. As a
cross-check, we will also compute the elastic scattering of a heavy quark with a longitudinal gluon, which allows us to determine the anomalous dimension
of the combination $c_{B_1}+c_{B_2}$. Furthermore, we compute the one transverse gluon-matrix element of the heavy quark, which allows us to cross-check the
anomalous dimensions of
$c_{W_1}$, $c_{W_2}$ and $c_{p'p}$. In the latter only irreducible diagrams enter the calculation. Note that $c_{B_1}$ has not been cross-checked in an
independent calculation because one would need to consider irreducible and reducible diagrams with at least three external transverse gluons. Such a
calculation is very hard and arguably not worth it because obtaining the correct structure of the $c_{B_1}$ vertex is non-trivial enough to be considered
as a strong cross-check. In general, external gluons and heavy quarks will be considered to be on-shell i.e. free asymptotic states, so the free
equations of motion (EOM) will be used throughout.

Note that we keep explicit the Wilson coefficients of the kinetic term for tracking purposes even though they are
protected by reparametrization invariance ($c_k=c_4=1$ to any order in perturbation theory) \cite{Luke:1992cs}. Also,
$c_{p'p}=c_F-1$ and the physical combination $\bar c_W=c_{W_1}-c_{W_2}=1$ are fixed by reparametrization invariance \cite{Manohar:1997qy}. We will
check by explicit calculation that these relations are satisfied at LL.

The Coulomb gauge will be used throughout this paper. On the one hand, this significantly reduces the number of diagrams but, on the other hand,
the complexity of each one of them increases. It also makes it difficult to use standard routines for computations of diagrams designed
for Feynman gauges and relativistic setups. However, since we are only looking for the pole, the calculation is feasible. The normalization of
the heavy quark field, gluon fields, the strong coupling $g$ and the Wilson coefficients $c_F$ and $c_S$ are needed. In the Coulomb gauge, they
read (we define $D=4+2\epsilon$):
\begin{eqnarray}
\nonumber
Z_{A^0}^{-1/2}=Z_g&=&1+\frac{11}{6}C_A\frac{\alpha}{4\pi}\frac{1}{\epsilon} -\frac{2}{3}T_Fn_f\frac{\alpha}{4\pi}\frac{1}{\epsilon} \,,
\quad Z_{\bf A}^{\frac{1}{2}}=1-\frac{1}{2}C_A\frac{\alpha}{4\pi}\frac{1}{\epsilon}-\frac{2}{3}T_Fn_f\frac{\alpha}{4\pi}\frac{1}{\epsilon}
\,,
\\
\nonumber
Z^2_gZ_{\bf A}&=&1+\frac{8}{3}C_A\frac{\alpha}{4\pi}\frac{1}{\epsilon}
\,,
\quad
Z_l=1+C_F\frac{\alpha}{4\pi}\frac{1}{\epsilon}
\,,
\quad
Z_h=1+\frac{{\bf p}^2}{m^2}\frac{4}{3}C_F\frac{\alpha}{4\pi}\frac{1}{\epsilon}
\,,
\end{eqnarray}
\begin{equation}
 c_{F,\,B}= c_{F,R} - c_{F,R} C_A\frac{\alpha}{4\pi}\frac{1}{\epsilon}\,,\;\;\;\;
 c_{S,\,B}= c_{S,R} - 2c_{F,R} C_A\frac{\alpha}{4\pi}\frac{1}{\epsilon}
\end{equation}
where
\begin{eqnarray}
  C_F=\frac{N_c^2-1}{2N_c}=\frac{4}{3}\,, \qquad C_A = N_c=3\,.
\end{eqnarray}
The subscript $B$ stands for bare and $R$ for renormalized quantities. Often the subscript $R$ will be removed in the following when it is
understood.

\subsection{QCD}
\label{sec:RGeq}

Let's consider the general case of QCD. First of all, for the pure gluonic sector, we have that $c_1^g$ is NLL, so it can be neglected.

The running of the set: $\{c_{W_1},c_{W_2},c_{B_1},c_{B_2}, c_{p'p}\}$ is determined from the topologies drawn in Fig.~\ref{PlotsHeavygluon1}. From
these, we generate all possible diagrams up to order $1/m^3$ by considering all possible vertices to the appropiate order in $1/m$ and/or kinetic
insertions, which correspond to the expansion of the non-static heavy quark propagator. Note that diagrams of lower order than $1/m^3$ must also
be considered, at least those that depend on the energy, as the use of the heavy quark EOM, $E= c_k \frac{{\bf p}^2}{2m}$, adds extra powers of $1/m$. This
generates around 200 diagrams (without taking into account permutations and crossing) in both cases: the elastic scattering with a transverse gluon and,
similarly, with a longitudinal gluon.

In the case of scattering with a transverse gluon, for diagrams proportional to $1/m^3$ operators, only the irreducible ones need to be considered. Note
that this is not true for the case of scattering with a longitudinal gluon because the Coulomb vertex does not add extra powers of $1/m$. When one
considers diagrams proportional to iterations of $1/m^2$ and/or $1/m$ operators one also has to consider reducible diagrams in both cases. One has
to keep in mind that Taylor expanding reducible diagrams in the energy can produce non-local terms which cancel at the end of the calculation and
all divergences can be absorbed by local counterterms that correspond to operators
of the Lagrangian\footnote{If we only compute irreducible diagrams we would need a larger number of operators, in particular those that vanish on shell.}.
It is also worth mentioning that we find that the sum of all reducible diagrams whose sub-irreducible diagram is $1/m$ or below
($1/m^2$ or below in the case of the scattering with a longitudinal gluon) cancel with the renormalization of the tree level reducible diagrams.
Therefore, non-local terms coming from expanding these diagrams in the energy vanish at all orders in the expansion.

Let's consider the calculation of the one tranverse gluon exchange, which has a peculiarity which deserves a comment. This calculation allows us to
determine the anomalous dimensions of $c_{W_1}$, $c_{W_2}$, $c_{p'p}$ and $c_S$. The necesary topologies to produce
the diagrams are shown in Fig. \ref{plot1t}. They produce around 50-60 diagrams without counting inverted ones. Note that we can only draw irreducible
diagrams in this case.  What is
interesting in this calculation is that one obtains a structure which does not look like any structure of the $1/m^3$ operators, i.e. the $1/m^3$ vertices
with a single transverse gluon. So at first sight,
it would look like a problem, since the divergence proportional to this structure could not be absorbed by any operator in the theory (leading one to suspect that there might be operators missing). However, this is not the case. The explanation is the following: in principle, one would consider
$c_S$ as an $\mathcal{O}(1/m^2)$ operator.
Nevertheless, the vertex with an external tranverse gluon is proportional to $k^0$, so it becomes $\mathcal{O}(1/m^3)$ after using the EOM. Therefore, in
order to determine the running of $c_S$ through the calculation of the one gluon exchange one must consider this operator
as an $\mathcal{O}(1/m^3)$ operator. Only in this way is the correct running of $c_S$ (expected from reparametrization invariance) obtained. So everything must
be made physical, meaning put on shell, in order to arrive to proper results. Note that the runnig of $c_S$ will appear also
in the determination of the running of Wilson coefficients at higher orders in $1/m$ if it is done through the calculation of the
one tranverse gluon matrix element of a heavy quark, because the EOM have corrections in $1/m$. In particular, it will appear at $\mathcal{O}(1/m^5)$.
This is important to keep in mind in future calculations.

The renormalization group equations for the unphysical set $\{c_{W_1},c_{W_2},c_{B_1},c_{B_2}, c_{p'p}\}$ in Coulomb gauge read:

$$\nu\frac{d}{d\nu}c_{W_1}=  \frac{\alpha}{\pi}\bigg(\frac{13}{12}c_{W_1}C_A  + \frac{7}{12}c_{W_2}C_A
- \frac{1}{4} c_{B_1} C_A - \frac{1}{8} c_{B_2} C_A
+ \frac{1}{24}c_{p'p} C_A $$
\begin{equation}
 + \frac{7}{24}c_S c_k C_A  - \frac{1}{6}c_S c_F C_A
 - \frac{1}{12}c_F c_k^2 (16C_F + 15C_A) + \frac{7}{8}c_F^2 c_k C_A \bigg)\,,
\end{equation}

$$\nu\frac{d}{d\nu}c_{W_2}= \frac{\alpha}{\pi} \bigg(\frac{7}{12}c_{W_1}C_A  + \frac{13}{12}c_{W_2}C_A
- \frac{1}{4} c_{B_1} C_A  - \frac{1}{8} c_{B_2} C_A
+ \frac{1}{24}c_{p'p} C_A $$
\begin{equation}
 - \frac{5}{24}c_S c_k C_A  - \frac{1}{6}c_S c_F C_A
 - \frac{1}{12}c_F c_k^2 (16C_F + 3C_A) + \frac{7}{8}c_F^2 c_k C_A \bigg)\,,
\end{equation}

$$\nu\frac{d}{d\nu} c_{B_1}=   \frac{\alpha}{\pi}\bigg( \frac{1}{6} c_{W_1} C_A + \frac{1}{6} c_{W_2} C_A
+ c_{B_1}C_A -  \frac{1}{3}c_{B_2} C_A
+ \frac{7}{12} c_{p'p} C_A$$
\begin{equation}
 + \frac{1}{12} c_S c_k C_A - \frac{1}{4} c_S c_F C_A
 + \frac{7}{6} c_F c_k^2 C_A  + \frac{7}{6} c_F^2 c_k C_A + \frac{3}{2} c_F^3 C_A \bigg)\,,
\end{equation}

$$\nu\frac{d}{d\nu} c_{B_2}
=   \frac{\alpha}{\pi} \bigg( c_{W_2} C_A
- \frac{1}{2}c_{B_1} C_A
+ \frac{7}{6}c_{B_2} C_A$$
\begin{equation}
 - \frac{4}{3} c_S c_k (4C_F + C_A)
 - \frac{1}{6} c_S c_F C_A
 + \frac{4}{3} c_F c_k^2 (2C_F - C_A)
 + \frac{2}{3} c_F^2 c_k C_A
 - \frac{3}{2} c_F^3 C_A \bigg)\,,
\end{equation}

\begin{equation}
 \nu\frac{d}{d\nu}c_{p'p}= \frac{\alpha}{\pi}\bigg(\frac{1}{2}c_{p'p} C_A  - \frac{1}{2}c_S c_k C_A + c_F c_k^2 C_A \bigg)\,.
\end{equation}
The renormalization group equations for the physical set $\{\bar c_{W}, \bar c_{B_1}, c_{B_2}, c_{p'p}\}$ read:

\begin{equation}
\label{cWbarrge}
 \nu\frac{d}{d\nu}\bar c_{W} = \frac{\alpha}{\pi} \bigg( \frac{1}{2}\bar c_{W} C_A
+ \frac{1}{2}c_S c_k C_A - c_F c_k^2  C_A \bigg)=0\,,
\end{equation}

$$\nu\frac{d}{d\nu} \bar c_{B_1} =
 \frac{\alpha}{\pi} \bigg( \frac{3}{2} \bar c_{B_1} C_A
+ \bar c_{W}C_A
- \frac{1}{12}c_{B_2} C_A
+ \frac{1}{2} c_{p'p} C_A$$
\begin{equation}
 - \frac{1}{2}c_S c_k C_A
 + \frac{1}{12} c_S c_F C_A
 + \frac{1}{3}c_F c_k^2 (8C_F + 11C_A)
 - \frac{7}{12} c_F^2 c_k C_A
 + \frac{3}{2} c_F^3 C_A \bigg)\,,
\end{equation}

$$\nu\frac{d}{d\nu} c_{B_2}
 = \frac{\alpha}{\pi}  \bigg( - \frac{1}{2}\bar c_{B_1} C_A
- \bar c_W C_A
+ \frac{7}{6}c_{B_2} C_A $$
\begin{equation}
 - \frac{4}{3} c_S c_k (4C_F + C_A)
 - \frac{1}{6} c_S c_F C_A
 + \frac{4}{3} c_F c_k^2 (2C_F - C_A)
 + \frac{2}{3} c_F^2 c_k C_A
 - \frac{3}{2} c_F^3 C_A \bigg)\,,
\end{equation}

\begin{equation}
 \nu\frac{d}{d\nu}c_{p'p}= \frac{\alpha}{\pi}\bigg(\frac{1}{2}c_{p'p} C_A  - \frac{1}{2}c_S c_k C_A + c_F c_k^2 C_A \bigg)\,.
\end{equation}
Where $\bar c_{W}$ and $\bar c_{B_1}$ come from the definitions given in Sec. \ref{Sec:Compton}. The last equality in Eq. (\ref{cWbarrge}) can be easily
deduced by using the relations between Wilson coefficients imposed by reparametrization invariance. When writing the counterterm of each Wilson coefficient
it is enough to know that the scaling with the renormalization scale is $\nu^{2\epsilon}$. It is quite remarkable that the RG equations depend only on
gauge-independent combinations of Wilson coefficients: $\bar c_{W}$, $\bar c_{B_1}$ and $c_{B_2}$. This is quite a strong check, as at intermediate
steps we get contributions from $c_{W_1}$, $c_{W_2}$ and $c_{B_1}$, which only at the end of the computation arrange themselves in gauge-independent combinations.

\begin{figure}[!htb]
	\includegraphics[width=0.95\textwidth]{LLcAic4cM1.png}
	\includegraphics[width=0.95\textwidth]{LLcAic4cM2.png}
\caption{Topologies contributing to the anomalous dimensions of the Wilson coefficients associated to $1/m^3$ spin-dependent operators in QCD.
The double-line represent the heavy fermion, whereas the curly line represents either a transverse or a longitudinal
gluon. Both external gluons are transverse or longitudinal depending on the kind of scattering we are considering. All diagrams are generated
from these topologies by considering all possible vertices up to ${\cal O}(1/m^3)$. Tree level diagrams should be understood
to be multiplied by Wilson coefficient, field and strong coupling counterterms.
\label{PlotsHeavygluon1}}
\end{figure}

\begin{figure}[!htb]
	\includegraphics[width=0.95\textwidth]{sd1t.png}
\caption{Topologies contributing to the one tranverse gluon exchange. All diagrams are generated from these topologies by considering all possible
vertices up to ${\cal O}(1/m^3)$. While the external gluon is transverse, internal gluons must be understood as either longitudinal
or transverse.}
\label{plot1t}
\end{figure}
\clearpage
\subsection{QED}
\label{sec:RGeqqed}

In this section we analyze the purely abelian case of QED. To do this, we just need to take the appropriate limit
of the results found in Sec. \ref{sec:RGeq} i.e. to take $C_F=1$, $C_A=0$ and $n_f=0$. Note that the operators proportional to $c_{B_1}$ and
$c_{B_2}$ do not appear now. The diagrams that contribute are the same drawn in Fig.~\ref{PlotsHeavygluon1} and Fig.~\ref{plot1t} disregarding non-abelian
diagrams.

The renormalization group equations read:

\begin{equation}
 \nu\frac{d}{d\nu}c_{W_1}=  - \frac{4}{3}c_F c_k^2 C_F \frac{\alpha}{\pi} \,,\;\;\;\;\;
 \nu\frac{d}{d\nu}c_{W_2}= - \frac{4}{3}c_F c_k^2 C_F \frac{\alpha}{\pi}\,,\;\;\;\;\;
 \nu\frac{d}{d\nu}c_{p'p}=0\,.
\end{equation}
This result is in agreement with the explicit single logs given in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}, where the calculation was
done in Feynman gauge. This is not that
strange; for instance,  the running of $c_D$ in QED happens to be equal in the Coulomb and Feynman gauges (see the discussion in
Ref. \cite{Pineda:2001ra}). The analysis done in Sec. \ref{Sec:Compton} suggests that the physical object is still $\bar c_W$, though. The results
obtained are in agreement with reparametrization invariance relations given in Ref. \cite{Manohar:1997qy} (recall that $c_F$ has no running in QED).

\section{Solution and numerical analysis}
\label{Sec:numerics}

The RG equations obtained in the previous section depend on a list of five Wilson coefficients
${\bf A}=\{ c_{W_1}, c_{W_2}, c_{B_1}, c_{B_2},c_{p'p} \}$. The running of $c_{p'p}$ has been found to be the same as that of $c_F$, as predicted
by reparameterization invariance, so we will not give an explicit expression. The remaining equations can be written more compactly
in a matrix form

\begin{equation}
\nu \frac{d}{d \nu} {\bf A}= \frac{\alpha}{\pi}({\bf M}  {\bf A}+{\bf F}(\alpha))
\,.
\end{equation}
The matrix ${\bf M}$ follows from the results of the previous section. We only need the running of $\alpha$ with LL accuracy:
\begin{equation}
 \nu   {{\rm d} \over {\rm d} \nu}   \alpha
\equiv
\beta(\alpha_s)
=
-2 \alpha
\left\{\beta_0{\alpha \over 4 \pi} + \cdots\right\}
\,,
\end{equation}
where
\begin{eqnarray}
  \beta_0&=&{11 \over 3}C_A -{4 \over 3}T_Fn_f\,,
\end{eqnarray}
and $n_f$ is the number of dynamical (active) quarks i.e. the number of light quarks. Recall that $n_f=0$ for the case we are studying.

In this approximation, the above equation can be simplified to
\begin{equation}
\frac{d}{d \alpha} {\bf A}= -\frac{2}{ \beta_0\alpha}({\bf M}  {\bf A} + {\bf F}(\alpha))
\,.
\end{equation}
It is useful to define $z \equiv \left(\frac{\alpha(\nu)}{\alpha(m)}\right)^{\frac{1}{\beta_0}}\simeq
1-\frac{1}{2\pi}\alpha(\nu)\ln (\frac{\nu}{m})$ and write the equation above as:

\begin{equation}
 \frac{d{\bf A}}{dz}=-\frac{2}{z}(\mathbf{M}{\bf A} + {\bf F}(z))\,.
\end{equation}
We also need the initial matching conditions at the hard scale, at tree-level. They have been determined
in Ref.~\cite{Manohar:1997qy} and read $c_k=c_F=c_S=c_{W_1}=c_{B_1}=1$
and $c_{W_2}=c_{p'p}=c_{B_2}=0$.

Note that the matching coefficient of the
kinetic term is protected by reparametrization invariance
($c_k=1$ to any order in perturbation theory) \cite{Luke:1992cs}.
Nevertheless, although we set them to 1 when solving the RG equations, we keep them explicit in the RG equations for
tracking purposes.

After solving the RG  equations we obtain the LL running of the Wilson coefficients associated to the $1/m^3$ spin-dependent operators
of the HQET Lagrangian. We obtain the following analytic results
for the unphysical set in Coulomb gauge:

$$ c_{W_1} = \frac{47}{82} - \frac{160C_F}{287C_A}
+ \left(\frac{1}{3}  + \frac{10C_F}{3C_A}\right)z^{-C_A}
- z^{-2C_A}
+ \frac{9}{2}z^{-3C_A}
+ \left(5 + \frac{22C_F}{7C_A}\right)z^{-\frac{7}{3}C_A}$$
$$+ \left(- \frac{517}{123}
 + \frac{14}{41}\sqrt{\frac{2}{5}}
 - \sqrt{\frac{5}{2}}
 + \frac{50}{123}\sqrt{10}
 - \frac{364C_F}{123C_A}
 - \frac{452C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A}$$
 \begin{equation}
 + \left( - \frac{517}{123}
 -\frac{14}{41}\sqrt{\frac{2}{5}}
 + \sqrt{\frac{5}{2}}
 -\frac{50}{123}\sqrt{10}
 - \frac{364C_F}{123C_A}
 + \frac{452C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{-\frac{1}{6}(16+\sqrt{10})C_A}\,,
\end{equation}\\

$$ c_{W_2} = -\frac{35}{82} - \frac{160C_F}{287C_A}
+ \left(\frac{1}{3}  + \frac{10C_F}{3C_A}\right)z^{-C_A}
- z^{-2C_A}
+ \frac{9}{2}z^{-3C_A}
+ \left(5 + \frac{22C_F}{7C_A}\right)z^{-\frac{7}{3}C_A}$$
$$+ \left(- \frac{517}{123}
 + \frac{14}{41}\sqrt{\frac{2}{5}}
 - \sqrt{\frac{5}{2}}
 + \frac{50}{123}\sqrt{10}
 - \frac{364C_F}{123C_A}
 - \frac{452C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A}$$
 \begin{equation}
 + \left( - \frac{517}{123}
 -\frac{14}{41}\sqrt{\frac{2}{5}}
 + \sqrt{\frac{5}{2}}
 -\frac{50}{123}\sqrt{10}
 - \frac{364C_F}{123C_A}
 + \frac{452C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{-\frac{1}{6}(16+\sqrt{10})C_A}\,,
\end{equation}\\

$$ c_{B_1} = \frac{55}{123} - \frac{1184C_F}{861C_A}
+ \left(- \frac{19}{9}  + \frac{44C_F}{9C_A}\right)z^{-C_A}
- z^{-2C_A}
- 6z^{-3C_A}
+ \left(10 + \frac{44C_F}{7C_A}\right)z^{-\frac{7}{3}C_A}$$
$$+ \left(- \frac{62}{369}
 - \frac{1034}{369}\sqrt{10}
 - \frac{1808C_F}{369C_A}
 - \frac{728C_F}{369C_A}\sqrt{10}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A}$$
 \begin{equation}
 + \left(- \frac{62}{369}
 + \frac{1034}{369}\sqrt{10}
 - \frac{1808C_F}{369C_A}
 + \frac{728C_F}{369C_A}\sqrt{10}\right)z^{-\frac{1}{6}(16+\sqrt{10})C_A}\,,
\end{equation}\\

$$c_{B_2} = -\frac{24}{41} - \frac{192C_F}{41C_A}
+ \left(\frac{11}{3} + \frac{32C_F}{3C_A}\right)z^{-C_A}
+ z^{-2C_A} + 18z^{-3C_A} $$
$$+\left( - \frac{1358}{123}
 + \frac{64}{41}\sqrt{\frac{2}{5}}
 + \frac{298}{123}\sqrt{10}
 - \frac{368C_F}{123C_A}
 + \frac{8C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A} $$
\begin{equation}
 + \left( - \frac{1358}{123}
 - \frac{64}{41}\sqrt{\frac{2}{5}}
 - \frac{298}{123}\sqrt{10}
 - \frac{368C_F}{123C_A}
 - \frac{8C_F}{123C_A}\sqrt{\frac{2}{5}} \right) z^{-\frac{1}{6}(16+\sqrt{10})C_A}\,.
\end{equation}
The solution for the physical set of Wilson coefficients read:

\begin{equation}
\label{cWbar}
 \bar c_{W} = 1\,,
\end{equation}

$$\bar c_{B_1} = -\frac{86}{123} - \frac{32C_F}{123C_A}
- \left( \frac{25}{9} + \frac{16C_F}{9C_A} \right)z^{-C_A}
+ z^{-2C_A}
- 15z^{-3C_A} $$
$$+ \left( \frac{3040}{369}
 - \frac{5077}{369}\sqrt{\frac{2}{5}}
 + \frac{376C_F}{369C_A}
 - \frac{928C_F}{369C_A}\sqrt{\frac{2}{5}}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A} $$
\begin{equation}
 + \left(\frac{3040}{369}
 + \frac{5077}{369}\sqrt{\frac{2}{5}}
 + \frac{376C_F}{369C_A}
 + \frac{928C_F}{369C_A}\sqrt{\frac{2}{5}}\right)z^{-\frac{1}{6}(16+\sqrt{10})C_A} \,,
\end{equation}

$$c_{B_2} = -\frac{24}{41} - \frac{192C_F}{41C_A}
+ \left(\frac{11}{3} + \frac{32C_F}{3C_A}\right)z^{-C_A}
+ z^{-2C_A} + 18z^{-3C_A} $$
$$+\left( - \frac{1358}{123}
 + \frac{64}{41}\sqrt{\frac{2}{5}}
 + \frac{298}{123}\sqrt{10}
 - \frac{368C_F}{123C_A}
 + \frac{8C_F}{123C_A}\sqrt{\frac{2}{5}}\right)z^{\frac{1}{6}(-16+\sqrt{10})C_A} $$
\begin{equation}
 + \left( - \frac{1358}{123}
 - \frac{64}{41}\sqrt{\frac{2}{5}}
 - \frac{298}{123}\sqrt{10}
 - \frac{368C_F}{123C_A}
 - \frac{8C_F}{123C_A}\sqrt{\frac{2}{5}} \right) z^{-\frac{1}{6}(16+\sqrt{10})C_A}\,.
\end{equation}
As can be seen, Eq. (\ref{cWbar}) satifies reparametrization invariance. We have proven by explicit calculation that, at LL, $c_{p'p}$ and
$\bar c_W$ satisfy the relations imposed by reparametrization invariance given in Ref. \cite{Manohar:1997qy}.

If we expand the above solutions in powers of $\alpha$ we can explicitely write the single log (it can also be obtained by trivial inspection of the
RG equations in Sec. \ref{Sec:RGE}). We obtain for the unphysical set that

\begin{equation}
\label{sl4}
c_{W_1} = 1 + \left( - \frac{4}{3}C_F + \frac{7}{12}C_A \right)\frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,,
\end{equation}

\begin{equation}
\label{sl5}
c_{W_2} =  \left(  -  \frac{4}{3}C_F + \frac{7}{12}C_A \right)\frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,,
\end{equation}

\begin{equation}
\label{sl6}
c_{B_1}= 1 + \frac{29}{6} C_A \frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,,
\end{equation}

\begin{equation}
\label{sl7}
c_{B_2} = -\left(\frac{8}{3}C_F + \frac{25}{6} C_A\right) \frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,,
\end{equation}
and for the physical set, that

\begin{equation}
\label{sl1}
 \bar c_{W} = 1 +{\cal O}(\alpha^2)\,,
\end{equation}

\begin{equation}
\label{sl2}
 \bar c_{B_1} = -1 + \left(  \frac{8}{3}C_F + \frac{11}{3} C_A \right)\frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,,
\end{equation}

\begin{equation}
\label{sl3}
 c_{B_2} = -\left(\frac{8}{3}C_F + \frac{25}{6} C_A\right) \frac{\alpha}{\pi}\ln\left(\frac{\nu}{m}\right)+{\cal O}(\alpha^2)\,.
\end{equation}

In Fig. \ref{Plots} one can see the above results when applied to the bottom heavy quark case, ilustrating the importance of incorporating large
logarithms in heavy quark physics. Only physical combinations and specific combinations that appear in physical observables, like Compton scattering, are
represented. We run the Wilson coefficients from the heavy quark mass to 1 GeV. For illustrative purposes, we take $m_b=4.73$ GeV and $\alpha(m_b)=0.215943$.

Concerning the numerical analysis, we observe that the effect due to the logarithms is large in general (not for QED however, where the only physical
combination that appears, $\bar c_W$, does not run). This is because the coefficients multiplying the
logs are large, in particular those that multiply the non-abelian coefficient $C_A$. We also observe that the LL resummation is saturated
by the single log in all cases except in the combination $\bar c_{B_1} + c_{B_2}$. Let us now discuss in more detail each individual Wilson coefficient. We
observe the following: $\bar c_{B_1}$ changes from -1 to -2.3 after running. The case of $c_{B_2}$ is rather similar, it goes from 0 to 1.45 after running. In
general, the effect of the resummation of logarithms is not quite large, but certainly sizable. It introduces a change of approximately 0.3 with
respect to the single log result. For the combination $\bar c_{B_1} + c_{B_2}$ the effect is very small, it goes from -1 to -0.99 even though it has a maximum in
which the value is -0.95. In this case the resummation of logs is important because the behaviour is not saturated by the single log.

\begin{figure}[!htb]

	\includegraphics[width=0.43\textwidth]{cB1b.png}

\hspace{6ex}
	\includegraphics[width=0.43\textwidth]{cB2.png}

	%
	\vspace{1ex}
	\includegraphics[width=0.43\textwidth]{cB1bpluscB2.png}
\caption{Running of the physical $1/m^3$ spin-dependent Wilson coefficients. The continuous line is the LL result with $n_f=0$ and the dashed line is
the single LL result which does not depend on $n_f$.
\label{Plots}}
\end{figure}

\section{Comparison with earlier work}
\label{Sec:Comparison}

The LL running of the Wilson coefficients associated to the $1/m^3$ operators of the HQET Lagrangian without considering light fermion effects was first
addressed in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}, where expressions for the anomalous dimension matrix and explicit
expressions for the Wilson coefficients with single log accuracy are given. As in Ref. \cite{chromopolarizabilities} for the spin-independent
case, we find that these results are mutually inconsistent, as the anomalous
dimension matrix produces different expressions for the single log result compared to the explicit single log expressions written in these references.

The basis of operators these results were obtained from is different from the basis used in this paper, so in order to
compare our results, we have to change the operator basis. This is done via field redefinitions, which at the order we are working in, is
equivalent to using the full equations of motion to order $1/m$. To this purpose, we use the HQET Lagrangian in a general frame,
Eq. (8) in Ref. \cite{Manohar:1997qy}\footnote{We take this opportunity to correct a missprint
in the term proportional to $c_{p'p}$, where the minus sign appearing there should be a plus sign in order to reproduce the Lagrangian Eq. (6) and
Eq. (7) in Ref. \cite{Manohar:1997qy}.}. We obtain the
following relations between the spin-dependent $1/m^3$ Wilson coefficients in the two bases:

\begin{equation}
 c_5^{(3)}= - c_{B_2} - c_k c_F^2 - c_S c_F\,,
\end{equation}
\begin{equation}
 c_6^{(3)} =  -c_{W_1} - c_{p'p} + c_k^2 c_F + \frac{1}{2}c_D c_F + \frac{1}{2}c_S c_k\,,
\end{equation}
\begin{equation}
 c_7^{(3)}= 2c_{W_2} - 2c_{p'p} - c_{B_1} + c_k c_F^2 + c_S c_F \,,
\end{equation}
\begin{equation}
 c_8^{(3)} =  -c_{W_1} - c_{p'p} + c_k^2 c_F + \frac{1}{2}c_D c_F + \frac{1}{2}c_S c_k\,,
\end{equation}
\begin{equation}
 c_9^{(3)} =  -c_{B_1} + c_k c_F^2 + c_S c_F\,,
\end{equation}
\begin{equation}
 c_{10}^{(3)} =  c_{p'p} + c_{B_1} - c_k c_F^2 - c_S c_F\,,
\end{equation}
\begin{equation}
 c_{11}^{(3)} =  c_{p'p} + c_{B_1} - c_k c_F^2 - c_S c_F\,.
\end{equation}
Note that $c_6^{(3)} = c_8^{(3)}$ and $c_{10}^{(3)}=c_{11}^{(3)}$. This is to be expected since it is well-known from Ref. \cite{Manohar:1997qy} that
there are five spin-dependent operators and five different Wilson coefficients, whereas in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}
there are seven operatos and seven different Wilson coefficients. Thereby, one must find that two Wilson coefficients have to be equal to another two.
In Ref. \cite{chromopolarizabilities} these relations between the Wilson coefficients  at $\mathcal{O}(1/m)$ and $\mathcal{O}(1/m^2)$ were also found:
\begin{eqnarray}
 c_1^{(1)} = c_k
\,,\qquad
 c_2^{(1)} = c_F
\,, \qquad
 c_1^{(2)} = -c_D
\,, \qquad
 c_2^{(2)} = c_S
\,.
\end{eqnarray}
In Ref. \cite{chromopolarizabilities} expressions for the correct anomalous dimension matrix for the spin-independent Wilson coefficients in the basis
used in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh} were given. However the situation for the spin-dependent case turns out to be more complicated, since
Wilson coefficients are gauge dependent. Because the calculation in these references was done in Feynman gauge and in this paper in Coulomb gauge, we can not
give a prediction for the anomalous dimension matrix in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh} in Feynman gauge (note that in the
spin-independent case there were also gauge dependent Wilson coefficients, but all gauge dependence came from $c_D$ and $c_M$, for which expressions are
well-known in Feynman gauge). Instead, to compare results, we compute the RG equations in our basis for physical quantities from the anomalous
dimension matrices given in Ref. \cite{Balzereit:1998jb}. To do this, one needs the inverse relations between the Wilson coefficients in
the two bases:

\begin{equation}
 c_{p'p} = c_9^{(3)} + c_{10}^{(3)}\,,
\end{equation}
\begin{equation}
 c_{W_1} = -c_6^{(3)} - c_9^{(3)} - c_{10}^{(3)} + c_1^{(1)\,2}c_2^{(1)} - \frac{1}{2}c_1^{(2)}c_2^{(1)} + \frac{1}{2}c_2^{(2)}c_1^{(1)}\,,
\end{equation}
\begin{equation}
 c_{W_2} = \frac{1}{2} c_7^{(3)} + \frac{1}{2}c_9^{(3)} + c_{10}^{(3)}\,,
\end{equation}
\begin{equation}
 c_{B_1} = -c_9^{(3)} + c_1^{(1)}c_2^{(1)\,2} + c_2^{(2)}c_2^{(1)}\,,
\end{equation}
\begin{equation}
 c_{B_2} = -c_5^{(3)} - c_1^{(1)}c_2^{(1)\,2} - c_2^{(2)}c_2^{(1)}\,.
\end{equation}
Firstly, note that the anomalous dimension matrix in Ref. \cite{Balzereit:1998jb} gives $c_6^{(3)}\neq c_8^{(3)}$. This already
disagrees with our results and with the explicit single log results given in Table II of that reference. We continue with the
comparison nonetheless. We take the expression for $c_6^{(3)}$, which is the one which minimizes the discrepancies. The RG equations read

\begin{equation}
\label{cpp}
 \nu\frac{d}{d\nu} c_{p'p} =\frac{\alpha}{\pi}\left( C_A c_F c_k^2 + \frac{1}{2}C_A c_{p'p} - \frac{1}{2}C_A c_S c_k\right)\,,
\end{equation}

\begin{equation}
\label{cWrg}
 \nu\frac{d}{d\nu}\bar c_W = \frac{\alpha}{\pi}\bigg( {\bf\frac{1}{6}}C_A c_D c_F - {\bf\frac{5}{12}}C_A c_F^3 - {\bf\frac{3}{4}}C_A c_F^2 c_k
 -{\bf\frac{1}{12}}C_A c_F c_k^2 - {\bf\frac{4}{3}}C_F c_F c_k^2 - {\bf\frac{1}{4}}C_A c_S c_k + \frac{1}{2}C_A \bar c_W\bigg)\,,
\end{equation}

$$ \nu\frac{d}{d\nu}\bar c_{B_1} = \frac{\alpha}{\pi}\bigg( \frac{3}{2}C_A \bar c_{B_1} - \frac{1}{12}C_A c_{B_2} -{\bf\frac{1}{3}}C_A c_D c_F
 + {\bf\frac{5}{6}}C_A c_F^3 + {\bf\frac{35}{12}}C_A c_F^2 c_k + {\bf\frac{11}{6}}C_A c_F c_k^2 $$
\begin{equation}
\label{cb1rg}
  + {\bf\frac{16}{3}}C_F c_F c_k^2 + \frac{1}{2}C_Ac_{p'p} - {\bf\frac{17}{12}}C_A c_F c_S + {\bf 1}C_A c_S c_k + C_A \bar c_W\bigg)\,,
\end{equation}

$$\nu\frac{d}{d\nu}c_{B_2} = \frac{\alpha}{\pi}\bigg( -\frac{1}{2}C_A \bar c_{B_1} + \frac{7}{6}C_A c_{B_2}
 - {\bf\frac{4}{3}}C_A c_F^2 c_k - \frac{4}{3}C_A c_F c_k^2 + \frac{8}{3}C_F c_F c_k^2 + {\bf\frac{4}{3}}C_A c_F c_S$$
\begin{equation}
  - \frac{4}{3}C_A c_S c_k -\frac{16}{3}C_F c_S c_k - C_A\bar c_{W} + {\bf 0} c_F^3\bigg)\,,
\end{equation}
where numbers in bold indicate a discrepancy with respect to our results. In general we find disagreement for all RG equations (even in QED) except
for Eq. (\ref{cpp}), which satisfies reparametrization invariance. Conceptually, the diagreement with Eqs. (\ref{cWrg}-\ref{cb1rg}) is important, as
these equations do not depend only on physical combinations of Wilson coefficients due to the explicit appearence of $c_D$, which is gauge dependent.
In addition, Eq. (\ref{cWrg}) does not satisfy reparametrization invariance.

On the other hand, it is remarkable that using the single log results given in Table II of Ref. \cite{Balzereit:1998vh} one finds agreement with our single
log results for the physical quantities $\bar c_W$, $\bar c_{B_1}$, $c_{B_2}$, given in Eqs. (\ref{sl1}-\ref{sl3}), and $c_{p'p}$, not presented
explicitely. However, we find disagreement for the unphysical quantities $c_{W_1}$, $c_{W_2}$ and $c_{B_1}$, given in Eqs. (\ref{sl4}-\ref{sl6}). If we
trust the explicit single logs presented in this reference, this is a clear indication these Wilson coefficients are gauge dependent.

\section{Conclusions}
\label{sec:conclusions}

We have computed the LL running of the Wilson coefficients associated to the spin-dependent $1/m^3$ operators of the HQET Lagrangian without light fermion
effects. We observe that reparametrization invariance relations are satisfied and that the running of physical quantities depend only on gauge-independent
quantities, as expected. Numerically, we observe that the running produces a large effect, except for the combination $\bar c_{B_1}+c_{B_2}$, which also
appears in Compton scattering. However, in this case, the resummation of large logarithms also happens to be important because the behaviour of this combination
is not saturated by the single log.

We have compared our results with the previous work done in Refs. \cite{Balzereit:1998jb,Balzereit:1998vh}. For the gauge invariant combinations we have
computed in our paper, the anomalous dimension matrix given in Ref. \cite{Balzereit:1998jb} yields different RG equations than those we found in
Sec. \ref{sec:RGeq}, and also different single logs as those given explicitely in that reference. Nevertheless, it is remarkable that
we find agreement with the explicit single logs given in these references.

These results are necessary building blocks for the determination of the pNRQCD Lagrangian with NNNLL accuracy. Even though
they appear not to be necessary to obtain the heavy quarkonium spectrum with NNNLL accuracy, nor the production and annihilation of heavy quarkonium
with NNLL precision, they are necessary at higher orders. Moreover, it may be important for future research in the determination of higher order
logarithms for NRQED bound states, like hydrogen and muonic hydrogenlike atoms.

\medskip

{\bf Acknowledgments} \\
We thank Antonio Pineda for useful discussions and for reading over the manuscript.
This work was supported in part by the Spanish grants FPA2014-55613-P and SEV-2016-0588.
RPB was supported for much of the duration of this work by the Barcelona
Institue of Science and Technology (BIST). RPB is currently supported by a Clarendon
Scholarship from the University of Oxford.

redpajama_set_name: RedPajamaArXiv


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Meritex Enterprises: back from the brink
Article | 1 November, 2008 11:06 AM | By Randel Carlock
In October US real estate investment company Meritex Enterprises, owned by the McNeely family, was named family business of the year by Minnesota Business magazine. While it is always significant to be honoured, the McNeely family's success is even more remarkable because 30 years ago the family business, then known as Space Center Inc, was the subject of a bitter lawsuit that nearly destroyed the family and the business.
Perhaps the best way to understand the scope of their troubles is to consider a story from local newspaper St Paul Pioneer Press Dispatch at the time:
Court orders liquidation for city warehouse firm
A Ramsey County District Court judge ruled Thursday that Space Center Inc should be placed in receivership and sold to resolve a long, bitter dispute among members of a family who control the St Paul warehouse company.
Space Center was founded in 1916 as St Paul Terminal Warehouse Co by Harry McNeely Sr (who died in 1968). Their children are now fighting for control of the company.
Donald G McNeely, son of the company's founder, is chairman of Space Center, president of a holding company, and head of more than 40 subsidiaries. His brother, Harry McNeely Jr, is vice president of the holding company, and a director of Space Center. Together, they own a majority of the company's stock.
The two men are being sued by the minority shareholders, led by their own sisters. They argued in court that the brothers had frozen them out of the company's management and any significant share of the profits, and that the brothers were running the company for their own benefit.
Specifically, they claimed that the brothers had 'avoided paying significant dividends, failed to disclose required information, and misused corporate assets for their own gain.' None of the minority shareholders has served on the company's board.
The lawyer representing the McNeely brothers said, 'If this decision of Judge Lynch is permitted to stand, it will be the demise of a company that provides jobs for 750 families. What we have here are minority shareholders who have lived most of their lives in Europe and just want to get money out of their holdings.
It was a classic family business battle of minority shareholders against majority shareholders, but with a painful sub-plot of sibling rivalry. "It's the old story of the [family] in the business and the [family] out of the business," said a long-time acquaintance, who later became a board member. "The people in the business say to the outside family members, 'Why are you giving us all this trouble? You're just sitting there collecting dividends!' The outsiders say, 'Well, we're family members too…'"
Harry McNeely Jr – one of the two sons and the youngest of the four siblings – had realised this all along, and had tried very hard to reconcile his sisters, Jean and Audrey, and older brother Donald. According to Harry Jr's children, the real conflict was between Donald – who had de facto control of the company – and his sisters over family issues not fully understood by anyone.
The business was simply the stage on which this family struggle was played out. Even during the court proceedings, Harry Jr continued to have dinner with his sisters, and kept trying to find a way to resolve the problem.
According to one of his daughters, it was a difficult period. "It was tough for Dad because he was trying to get everybody back at the table rather than [taking the dispute to] a courtroom," she said. "It was hard because he is a real family man, and his family was having a terrible fight. This had been going on for years, in fact. The aunts would fly in from Europe and make waves, then leave. He tried to be the peacemaker."
There are always as many sides to a family story as there are characters in the drama. Harry Sr had taken his two sons into the company as shareholders, but decided to make provisions for his two daughters in the form of a generous cash settlement, making them completely independent (with no financial or legal ties to the family business).
At the reading of Harry Sr's will a few days after the funeral his daughters Jean and Audrey, realising that they had been left out of his will as he had told them they would be, hired a law firm to contest the will and sue their mother and brothers for unduly influencing their father. Their mother, facing a lawsuit from her daughters, agreed to make each of them 10% shareholders.
"The sisters' issue was that the minority shareholders had no representation on the board," explained one of Harry Jr's daughters. "As a result, the company never paid dividends; they had no access to liquidity, and were never a part of planning and decision-making. They wanted to know, 'What is the company doing? Where is it going?' but they were ignored.
"It came down to a difference between brothers. My father tried to address those issues, but Don would not entertain any of the sisters' grievances. He wouldn't talk about them, refused to deal with his sisters and considered them a pain. His attitude seemed to be that they had no rights and no ability to take any action against him.
"The family members simply had different needs. You have to listen and respect those needs in a business family, but that wasn't happening with the siblings in my father's family. And that is what led inevitably to the lawsuit. Emotions were heightened– and then, you know how Americans are: 'hit that speed dial to the lawyer!'"
Before instituting the lawsuit, the sisters appealed to their uncle and Paul Frenzel, Harry Sr's retired former business partner and long-time minority shareholder to join them. As a result, a family ownership conflict had become a very public courtroom drama.
It was a terrible period for Harry Jr and his children who watched as their family legacy burned to ashes. "I was in my office – the case was being heard at the district court nearby – when one of my colleagues walked in and said, 'You're never going to believe what I just heard,'" recalled Harry Jr.
"I sat down and said, 'Okay, tell me.' And he said, 'Your brother Don, on the witness stand, swore under oath that he didn't have any sisters. And they were sitting in the courtroom in front of him.'"
That was in the first ten minutes of the trial, and it never got any better. Immediately following the court decision the two McNeely brothers, who served as CEO and vice president, developed a strategy to save the business by liquidating assets and transferring property to settle the judgment.
The company survived the bitter lawsuit but it had poisoned Donald's thinking about family businesses. He later called a meeting of his and his brother's children to declare that Space Center was no longer a family business and that none of the third generation would be involved. This decision is reported to have been made without consulting Harry Jr.
"When you think about the generational differences and goals (between the brothers), you could look back and say we should have just ended our relationship with him right then and there. But our family tie was too strong," stated one of Harry Jr's daughters. However, both Donald and Harry Jr wanted to put the lawsuit behind them and return to business as usual as soon as possible.
Soon after the lawsuit concluded, Donald started a process that would split the family business with each of the two brothers having separate holdings. The goal was to divide Space Center into two businesses. In December 1989, Space Center held its last board meeting as a family company and approved a separation into two distinct business entities. Donald used the non-family management to divide the company's assets into two equal as possible companies and asked Harry Jr to chose first.
The McNeely story contains many important lessons about the power of family leadership that is driven by a meaningful family vision that is both espoused and enacted. After the businesses were split, Harry Jr still believed that the McNeelys were a business family and that working together could create greater economic value and stronger family connections. His vision was more than an espoused dream because it was supported by several interrelated behaviours that he acted upon.
First, he realised that recreating a family business after two break ups required the full commitment of his children – and eventually their spouses and children. This was not easy after what the family had experienced but Harry Jr always presented family participation as an option not an obligation.
Second, the lawsuits had clearly taught him about the difficulties of thinking as individuals as opposed to stewards working for the interests of all the stakeholders. He taught his children to think about the future for their children and that the measure of each generation's success was their children's success.
Third, he realised that he and his siblings did not know how family businesses worked, the importance of governance structures such as boards or the critical skills like communications.
All of these weaknesses combined to create conflicts that had eventually overwhelmed the family and business. He set as one of his goals developing his children's knowledge and potential talents for family ownership and leadership.
Fourth, and perhaps most important, he learnt the importance of being authentic. Business families are often good at coming up with great ideas and talking about the family business but less good at acting on the tough decisions and plans.
Harry Jr struggled like any other senior generation family member. Becoming the CEO-owner in his late 60s meant that from his first day in charge he was past his sell by date and had to work on succession. His children also admit that there were many times when they would throw up their hands in frustration because of delays or changes in his thinking.
These struggles only served to push Harry Jr to new ways of thinking and acting. He formed a board of directors with a majority of independent directors, he hired outside advisors to help coach his family, he allowed each of his children to serve as a rotating board members to experience governance first hand and he began the practice of holding family meetings where all of his children were invited to discuss issues and share their perspectives.
He even managed the succession process that resulted in his son returning to the family business after many years as a bank executive and eventually being named CEO by the independent board of directors. In the end he never gave up on his vision for McNeely family ownership and leadership of the business his parents had founded.
The concluding part of the McNeely story goes back to beginning and the vision of the founding generation. Harry Sr and his wife created the McNeely Family Foundation to benefit the local area; for example it provides grants for education, human services, the environment, the arts and community betterment. The foundation also matches employees' gifts to their charitable organisations, and awards educational scholarships to their children, and sponsors fund-raising for catastrophic events such as the attack of 11 September 2001.
The senior McNeelys probably never intended that their act of philanthropy would develop into a vehicle to reunite the four family branches of their own family but under Harry Jr's leadership that is exactly happened.
"During my father's tenure as chair of the McNeely Foundation, he continued the involvement of Donald's family branch on the foundation board and along with two of his own children. He also added the only child of his sister, who was also the heir of his other sister who was childless," explained Harry Jr's daughter Shannon.
"In effect, he had all the descendents of his generation represented within the foundation, all working together as his generation was never able to do. I think that he satisfied not only his desire to see the extended family sharing the legacy of the foundation, but also made amends for the transgressions of his generation and their inability to mend their differences peacefully during my grandmother's lifetime.
"I know that the family lawsuit, and even more the personal bitterness among some of her children, was a source of great sadness to my grandmother until the day she died. Our regenerated unity of families and purposes—fuelled by a son's desire on a deeply personal level to set things right for his mother – is a symbolic statement to all McNeelys and the outside world that we have moved beyond our history," she said.
Business families, especially founders, often doubt the value of family business planning tools such as a shared vision for improving business performance and strengthening family harmony and question if it really works. The McNeely family story clearly demonstrates that it not only works, it wins awards.
Campden FB No41 Nov/Dec 2008
Related terms: Meritex, FB People, Family Business
Wilmington Trust
de Visscher & Co
Withers Bergman
Merrill Lynch Wealth Management
Relative Solutions
Edgar Brandt Advisory SA


The 42nd Annual the Living Way of the Cross will reenact several scenes of Jesus Christ final days along a procession route that begins at Providence of God at 8:30 a.m. Friday, April 19.
PILSEN — To celebrate a longstanding tradition, hundreds of Catholics are expected to gather along 18th Street for Good Friday in Pilsen next week.
The 42nd Annual the Living Way of the Cross will reenact several scenes of Jesus Christ's final days along a procession route that begins at Providence of God, 717 W. 18th St., at 8:30 a.m. Friday, April 19.
The Pilsen Via Crucis procession will head westbound on 18th Street before arriving at Harrison Park, where organizers will reenact Jesus Christ's crucifixion.
The procession will then head to St. Adalbert Catholic Church, 1650 W. 17th St., for a final prayer ahead of Easter Sunday.
At 3 p.m., a celebration of the Last Seven Words will be held at Providence of God, followed by Holy Friday Liturgy at St. Procopius Catholic Church, 1641 S Allport St. at 7 p.m.
Pilsen's Via Crucis has been held since 1977.


Aubrey Marcus Wellness Force Episode 123: With the volume of noise in our modern world that distracts and arouses the egoic mind, how do we awaken more consciousness so we can discover our deeper purpose?
We often fall prey to short-term solutions like drugs, alcohol, or social media to cover up the real feelings and desires we hold in our heart. While these mental and emotional band-aids make us feel better in the moment, they don't actually get to root of the deeper issue.
How can we shift our consciousness and overcome the allure of the egoic mind's temporary band-aids to powerfully show up and own the day?
On this episode of Wellness Force Radio, we explore this topic and much more with Aubrey Marcus, founder of Onnit. During this exclusive, in-person interview, Aubrey uncovers the tools and strategies we need to reconcile our egoic delusions, shed limiting beliefs, and heighten our conscious awareness.
When we tap into our conscious awareness we can reconcile our egoic delusions, shed limiting beliefs, and heighten our intuition.
We can use the breath as an efficient and elegant solution to alter our consciousness.
Developing a healthy sense of detachment will help us enjoy the simple pleasures of the world, without letting them dictate our lives and emotions.
I've always believed to play any game well, you best know what all the buttons do. As an entrepreneur, athlete, and consciousness explorer I've spent a lifetime pressing all the proverbial buttons in the game of life, and the Aubrey Marcus Podcast is a venue to bring forward the lessons learned from triumph and disaster. We bring in world class guests to discuss how you can support your body, turn resistance to assistance, harness the potential of your mind and emotions, and cultivate a battle tested spirituality without all the BS. But most importantly we have some fun while we do it. Follow me on social @AubreyMarcus, and for more on the tools of human optimization, check out @Onnit.
as a nutritional supplements brand based on a holistic health philosophy he calls Total Human Optimization. Aubrey Marcus has since grown Onnit into an industry leader, providing innovative peak performance supplements, foods, fitness equipment, and apparel.
Aubrey graduated from the University of Richmond in 2004 with a degree in philosophy and classical civilization. He soon founded a boutique marketing firm, specializing in brand development and eCommerce. It was during these seven years running the agency that Aubrey conceived of Onnit.
as a multi-sport athlete — as well as his background in ancient philosophy — his goal was to create a company that empowered people to achieve their fullest human potential. With the launch of the firm's flagship supplement Alpha BRAIN in 2011, Onnit was born.
In addition to the range of products offered on Onnit.com, Onnit is sole owner of Black Swan Yoga, four-time winner of the Best Yoga in Austin. Austin is also home to the Onnit Academy Gym, featuring DeFranco's Gym and 10th Planet Jiu Jitsu at the Onnit Academy.
Aubrey is currently the host of two celebrated podcasts: The Aubrey Marcus Podcast and the Total Human Optimization. He regularly makes appearances on a variety of media outlets, including the Joe Rogan Experience, The Jason Ellis Show, Dr. Oz, The Doctors, and Entrepreneur.


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A shot of design for healthcare brands
Terms like "metered dosage" and "clinical trial" are staples of healthcare products. But for savvy marketers competing in the evolving over-the-counter (OTC) pharmaceutical industry, concepts such as "sensory branding" and "transformative experience" are becoming essential additions to the list.This month, Shelf Impact! examines two OTC packages that embody these concepts through sensory perception, a marketing tactic rarely seen in healthcare packaging.
• GlaxoSmithKline (GSK) Consumer Healthcare, Moon Township, PA, is marketing its new alli OTC weight-loss capsules in a consumer-friendly starter kit whose design delivers a sensory experience by presenting the brand as the consumer's ally during a weight-loss program.
"We got very deep into the consumer experience, and we found that weight loss is a very emotionally charged category," says Donna Sturgess, global head of innovation at GSK Consumer Healthcare. "We needed alli to be an honest voice and a transparent brand—here's what you can expect if you follow the instructions."
Ideo developed packaging to gently guide consumers in the product's use. GSK markets alli in a starter kit—a two-piece plastic container and lid. Inside the container, a white thermoformed tray contains a bottle of 60-mg tablets in the 60-, 90-, or 120-count sizes, a pill-carrying case, product usage pamphlets, a daily journal, a calorie and fat counter, and Quick Facts cards. The kit's graphics card provides information for accessing a personalized diet action plan at www.myalli.com.
The primary container and tray also work on a sensory level. The white tray holding the product and collateral materials is easily viewed through the transparent lid. They are meant to be emotionally reflective as product users transform themselves during the dieting process.
"It puts forth a canvas so you can see yourself and create your own identity," Sturgess says.
The bottle label prominently displays the four-color alli brandmark. Different colors in the brand name correspond to emotional cornerstones of understanding the product and sustaining a product-use routine: What is alli? How does it work? What's the plan? Are you ready?
• The second OTC pharmaceutical package, designed for the Plan B emergency contraceptive, reflects regulatory changes that now make the drug available in nonprescription form for women 18 and older. Barr Pharmaceuticals, Pomona, NY, markets the drug in packaging that is adaptable both behind the pharmacy counter and on the store shelf, saving the company money with a single package. The carton's soothing colors and focus on product benefits give women peace of mind about their purchase.
Barr decided that women 18 and older were old enough to purchase the product on the store shelf without a pharmacist's guidance, but needed a package to provide functional benefits and reduce purchase anxiety.
IQ Design helped create the carton. The dual-label package contains two pieces. The outer sleeve, believed to be SBS, includes white space on the back panel for the prescription label when the drug is sold in prescription form to women 17 and younger. A hinged, billfold carton that also looks to be SBS contains two tablets enclosed with clear film inside a die-cut window on the billfold's right panel.
The package, containing two 0.75-mg levonorgestrel tablets, makes Plan B visually approachable for consumers, says Carol Cox, Barr spokesperson.
"This was a deliberate decision for several reasons," Cox says. "First, shelf space behind the counter in pharmacies is limited, and some pharmacies would not be able to accommodate shelving two separate products. Second, having a single package for the OTC and Rx product minimizes confusion for consumers and pharmacists. Third, the package has a new National Drug Code number from the previously Rx-only product."
The carton, from Sharp Corp., also contains prescribing information and a patient information booklet explaining how and when to consume the tablets. The design's blue-violet background gives way to a circular graphic using darker tones of the same colors. A side-by-side bright green swoosh bleeds off the carton.
For package designers: online package image gallery
Red Lion: Data station support
Panel PC systems


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Tag: 娱乐地图KT
Every profile update still had to begin with "is,Not only this the additional Court in Goa in which this case is being heard has even expressly prohibited this video to be shown to the public Obviously the channel pays no heed to the law and has no qualms about airing evidence in a rape case The hypocrisy here has sprouted a whole new ugly head: Times Now didn't just break the law it also went against its own previous editorial assertion that there was reasonable doubt the videos were doctored and more importantly were released by Tejpal himself to sway opinion in his favour Some social media commentators were virtually scratching their heads in confusion wondering why Times Now was airing footage that would potentially make a case for Tejpal or at least enervate his "liberal" support base when he's been such a popular enemy of Times Now's favoured right-wing for so long Others asserted that this was a concerted effort to deflect attention from the recent Cobrapost sting which showed how the Times Group among many other media houses will happily accept money in exchange for publishing certain kinds of political stories that support extremist agendas Journalist and author Kalpana Sharma caustically tweeted to Times Now that in "pretending you are for the survivor you are making her relive the horror I know that you're not in the business of journalism but this has touched a new low" Journalists Geeta Seshu and Ranjona Bannerjee suggested that the episodes on the Tejpal tapes were a distraction from Times Now's involvement in the Cobrapost sting with Bannerjee even calling it a "cheap sleazy and disgusting" move Activist and secretary of the All India Progressive Women's Association Kavita Krishnan also pointed out how the channel has actually illegally aired the court's property and in doing so certainly has not helped the survivor The National Women in Media Network has also published a strongly worded statement detailing which laws and guidelines laid down in the Code of Ethicsand Broadcasting Standards and News Broadcasting Standards regulations of the News Broadcasters Association (NBA) the channel has broken Soviet film director and theorist Lev Kuleshov believed that a careful juxtaposition of completely unrelated shots could be used to manipulate the emotions of the audience He once edited a film that showed viewers the same shot of a man's expressionless face alternated with shots of a bowl of soup a coffin and a beautiful woman Viewers weren't aware that the shot of the man's face remains unchanged and automatically felt that he looked hungry when he looked at the soup sad when looking at the coffin and happy (or something) when looking at the woman This is called the Kuleshov effect In the same way if you see a picture of a child and apple with a headline about world hunger you're bound to feel the child looks hungry A picture of a straight-faced woman and a headline about widowhood makes you think she looks sad And if you see the very same straight-faced woman alongside a headline about dominant businesswomen you'll probably read her expression as a sign of her competitiveness competency and martial dedication to work It feels like Times Now forgetting that it is in the business of news attempted a rare toxic blend of the Kuleshov effect and kuchh bhi: Manipulating the emotions of the audience using the same piece of evidence just accompanied by radically and almost laughably different commentary innuendo and analyses in an attempt to manipulate viewers into believing exactly what the channel wanted the law and consistency be damned Perhaps in response to the subsequent outrage Times Now has now deleted the video from the online version of the story making it clear that the channel is now fully aware that it shouldn't have broadcast it in the first place Too late now though isn't it The Ladies Finger (TLF) is a leading online women's magazine delivering fresh and witty perspectives on politics culture health sex work and everything in between Jonathan won clearly in the South-West, "I want to wear his initial / On a chain round my neck." For now. read more
Posted in wlvawkzlTagged 上海后花园LC 上海龙凤419FR 娱乐地图CT 娱乐地图KTLeave a comment


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Q: how to fetch data with react-app from node,express-server, when react-app is called from server I have a react-app which is called from my node-server. But the react-app also fetches data from the server. The problem is, that the react-app is just able to fetch data from the server, when this code is deleted:
app.get('/*', function (req, res) {
res.sendFile(path.join(__dirname, '../build', 'index.html'));

})
Because all requests are going to this app.get('/*'..), even when the react-app trys to fetch images from the server like this:
app.post('/images',express.static('images'));

Because all requests are going to the above function, so its not possible to fetch the images anymore.
Thanks for your help.

A: You should use
app.use(express.static('images'))

Instead of adding a route. Then you need to add static as prefix to the http path. You could do the same with your react files.
check https://expressjs.com/en/starter/static-files.html

redpajama_set_name: RedPajamaStackExchange


Two gunmen were shot and killed by police on Sunday after they opened fire on security guards at a Muhammad cartoon contest and exhibit in the Dallas suburb of Garland, Texas. The event was organized by conservative firebrand Pamela Geller and featured the anti-immigration Dutch politician Geert Wilders as keynote speaker.
Police were not releasing many details as of Sunday night, but the city of Garland's Facebook page carried a statement saying that one security officer at the heavily-patrolled event was shot in the leg before other officers returned fire, killing the two assailants. Local news station WFAA reported that police were also searching the area for a vehicle that may contain explosives.
We will have more on this story as it develops!